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Ellipse in a Circle Locus

Ellipse in a Circle Locus
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2015-03-05 10:34
CircleGeometric ConstructionLocus
In collections Conic Section Collection
This example demonstrates the dynamic locus of an ellipse within a circle. It involves core mathematical concepts such as circle, ellipse, polynomial functions, scalene triangles, difference and slope, geometric mean, and median value. The construction utilizes GeoGebra commands like Circle, Point, Segment, PointIn, LineBisector, Intersect, Angle, and Ellipse. It is suitable for high school students studying analytical geometry and geometric constructions to understand trajectory and dynamic geometric relationships.

GeoGebra Commands & Parameters

  1. Circle(O, B) → c
  2. Point(c) → C
  3. Segment(O, C) → a
  4. PointIn(b) → F
  5. Segment(F, C) → d
  6. LineBisector(d) → e
  7. Intersect(e, a) → L
  8. Intersect(e, d) → D
  9. Angle(L, D, F) → α
  10. Segment(L, F) → g
  11. Segment(C, D) → i
  12. Segment(D, F) → k
  13. Ellipse(O, F, L) → f

AI Drawing Prompt Reference

Draw a circle and a point inside it. Connect the center of the circle to the point to form a line segment. Take a point on this line segment and connect it to the point on the circle to form another line segment. Find the perpendicular bisector of this line segment, which intersects the first line segment and the new line segment at two points. Connect these intersection points to the point on the circle and to each other. Finally, draw an ellipse using the center of the circle, the point on the line segment, and one of the intersection points to show the dynamic locus of the ellipse within the circle.
The prompt above was compiled from the original drawing commands and is for reference only.